Nationality German Role Mathematician Name Lazarus Fuchs | Doctoral advisor Karl Weierstras Alma mater University of Berlin Residence Germany | |

Born 5 May 1833
Moschin, Prussia ( 1833-05-05 ) Institutions University of Greifswald
University of Heidelberg
University of Berlin
University of Gottingen Doctoral students Gerhard Hessenberg
Edmund Landau
Hermann Schapira
Ludwig Schlesinger
Issai Schur
Theodor Vahlen
Ernst Zermelo Known for Fuchsian groups
Picard–Fuchs equation
Fuchs's theorem Died April 26, 1902, Berlin, Germany Education Humboldt University of Berlin Books The Blueprint: Success Is a State of Mind, Partially Ordered Algebraic Systems Influenced Henri Poincare, Camille Jordan, Felix Klein Similar People Karl Weierstrass, Henri Poincare, Ernst Kummer, Felix Klein, Edmund Landau |

**Lazarus Immanuel Fuchs** (5 May 1833 – 26 April 1902) was a German mathematician who contributed important research in the field of linear differential equations. He was born in Moschin (Mosina) (located in Grand Duchy of Posen) and died in Berlin, Germany. He was buried in Schöneberg in the St. Matthew's Cemetery. His grave in section H is preserved and listed as a grave of honour of the State of Berlin.

He is the eponym of Fuchsian groups and functions, and the Picard–Fuchs equation. A singular point *a* of a linear differential equation

is called Fuchsian if *p* and *q* are meromorphic at the point *a*, and have poles of orders at most 1 and 2, respectively. According to a theorem of Fuchs, this condition is necessary and sufficient for the regularity of the singular point, that is, to ensure the existence of two linearly independent solutions of the form

where the exponents

Another well-known result of Fuchs is the *Fuchs's conditions*, the necessary and sufficient conditions for the non-linear differential equation of the form

to be free of movable singularities.

Lasarus Fuchs was the father of Richard Fuchs, a German mathematician.

## Selected works

*Über Funktionen zweier Variabeln, welche durch Umkehrung der Integrale zweier gegebener Funktionen entstehen*, Göttingen 1881.

*Zur Theorie der linearen Differentialgleichungen*, Berlin 1901.

*Gesammelte Werke*, Hrsg. von Richard Fuchs und Ludwig Schlesinger. 3 Bde. Berlin 1904–1909.